#importing libraries to perform EDA
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import matplotlib.gridspec as gridspec
import matplotlib.cm as cm

pip install datetime

Requirement already satisfied: datetime in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (5.5)
Requirement already satisfied: zope.interface in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from datetime) (6.4.post2)
Requirement already satisfied: pytz in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from datetime) (2024.1)
Requirement already satisfied: setuptools in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from zope.interface->datetime) (70.3.0)
Note: you may need to restart the kernel to use updated packages.

[notice] A new release of pip is available: 24.1.2 -> 24.2
[notice] To update, run: python.exe -m pip install --upgrade pip

pip install statsmodels

Requirement already satisfied: statsmodels in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (0.14.2)
Requirement already satisfied: numpy>=1.22.3 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from statsmodels) (2.0.0)
Requirement already satisfied: scipy!=1.9.2,>=1.8 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from statsmodels) (1.14.0)
Requirement already satisfied: pandas!=2.1.0,>=1.4 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from statsmodels) (2.2.2)
Requirement already satisfied: patsy>=0.5.6 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from statsmodels) (0.5.6)
Requirement already satisfied: packaging>=21.3 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from statsmodels) (23.2)
Requirement already satisfied: python-dateutil>=2.8.2 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from pandas!=2.1.0,>=1.4->statsmodels) (2.8.2)
Requirement already satisfied: pytz>=2020.1 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from pandas!=2.1.0,>=1.4->statsmodels) (2024.1)
Requirement already satisfied: tzdata>=2022.7 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from pandas!=2.1.0,>=1.4->statsmodels) (2024.1)
Requirement already satisfied: six in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from patsy>=0.5.6->statsmodels) (1.16.0)
Note: you may need to restart the kernel to use updated packages.

[notice] A new release of pip is available: 24.1.2 -> 24.2
[notice] To update, run: python.exe -m pip install --upgrade pip

pip install holidays

Requirement already satisfied: holidays in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (0.52)
Requirement already satisfied: python-dateutil in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from holidays) (2.8.2)
Requirement already satisfied: six>=1.5 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from python-dateutil->holidays) (1.16.0)
Note: you may need to restart the kernel to use updated packages.

[notice] A new release of pip is available: 24.1.2 -> 24.2
[notice] To update, run: python.exe -m pip install --upgrade pip

df1 = pd.read_csv("C:/Users/Ramasish Chatterjee/Downloads/train(1).csv") #to read the csv file saved

df=df1

df.head() #to get top 06 values

	datetime	season	holiday	workingday	weather	temp	atemp	humidity	windspeed	casual	registered	count
0	2011-01-01 00:00:00	1	0	0	1	9.84	14.395	81	0.0	3	13	16
1	2011-01-01 01:00:00	1	0	0	1	9.02	13.635	80	0.0	8	32	40
2	2011-01-01 02:00:00	1	0	0	1	9.02	13.635	80	0.0	5	27	32
3	2011-01-01 03:00:00	1	0	0	1	9.84	14.395	75	0.0	3	10	13
4	2011-01-01 04:00:00	1	0	0	1	9.84	14.395	75	0.0	0	1	1

df.shape

(10886, 12)

df.columns

Index(['datetime', 'season', 'holiday', 'workingday', 'weather', 'temp',
       'atemp', 'humidity', 'windspeed', 'casual', 'registered', 'count'],
      dtype='object')

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10886 entries, 0 to 10885
Data columns (total 12 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   datetime    10886 non-null  object 
 1   season      10886 non-null  int64  
 2   holiday     10886 non-null  int64  
 3   workingday  10886 non-null  int64  
 4   weather     10886 non-null  int64  
 5   temp        10886 non-null  float64
 6   atemp       10886 non-null  float64
 7   humidity    10886 non-null  int64  
 8   windspeed   10886 non-null  float64
 9   casual      10886 non-null  int64  
 10  registered  10886 non-null  int64  
 11  count       10886 non-null  int64  
dtypes: float64(3), int64(8), object(1)
memory usage: 1020.7+ KB

df.head()

	datetime	season	holiday	workingday	weather	temp	atemp	humidity	windspeed	casual	registered	count
0	2011-01-01 00:00:00	1	0	0	1	9.84	14.395	81	0.0	3	13	16
1	2011-01-01 01:00:00	1	0	0	1	9.02	13.635	80	0.0	8	32	40
2	2011-01-01 02:00:00	1	0	0	1	9.02	13.635	80	0.0	5	27	32
3	2011-01-01 03:00:00	1	0	0	1	9.84	14.395	75	0.0	3	10	13
4	2011-01-01 04:00:00	1	0	0	1	9.84	14.395	75	0.0	0	1	1

df.tail()

	datetime	season	holiday	workingday	weather	temp	atemp	humidity	windspeed	casual	registered	count
10881	2012-12-19 19:00:00	4	0	1	1	15.58	19.695	50	26.0027	7	329	336
10882	2012-12-19 20:00:00	4	0	1	1	14.76	17.425	57	15.0013	10	231	241
10883	2012-12-19 21:00:00	4	0	1	1	13.94	15.910	61	15.0013	4	164	168
10884	2012-12-19 22:00:00	4	0	1	1	13.94	17.425	61	6.0032	12	117	129
10885	2012-12-19 23:00:00	4	0	1	1	13.12	16.665	66	8.9981	4	84	88

df.describe(include='all')

	datetime	season	holiday	workingday	weather	temp	atemp	humidity	windspeed	casual	registered	count
count	10886	10886.000000	10886.000000	10886.000000	10886.000000	10886.00000	10886.000000	10886.000000	10886.000000	10886.000000	10886.000000	10886.000000
unique	10886	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
top	2012-12-19 23:00:00	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
freq	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
mean	NaN	2.506614	0.028569	0.680875	1.418427	20.23086	23.655084	61.886460	12.799395	36.021955	155.552177	191.574132
std	NaN	1.116174	0.166599	0.466159	0.633839	7.79159	8.474601	19.245033	8.164537	49.960477	151.039033	181.144454
min	NaN	1.000000	0.000000	0.000000	1.000000	0.82000	0.760000	0.000000	0.000000	0.000000	0.000000	1.000000
25%	NaN	2.000000	0.000000	0.000000	1.000000	13.94000	16.665000	47.000000	7.001500	4.000000	36.000000	42.000000
50%	NaN	3.000000	0.000000	1.000000	1.000000	20.50000	24.240000	62.000000	12.998000	17.000000	118.000000	145.000000
75%	NaN	4.000000	0.000000	1.000000	2.000000	26.24000	31.060000	77.000000	16.997900	49.000000	222.000000	284.000000
max	NaN	4.000000	1.000000	1.000000	4.000000	41.00000	45.455000	100.000000	56.996900	367.000000	886.000000	977.000000

DATA CLEANING

df.duplicated().any()

np.False_

parts = df['datetime'].str.split(' ', n=2, expand=True)
df['date'] = parts[0]
df['time'] = parts[1].str[:2].astype('int')
parts = df['date'].str.split('-', n=2, expand=True)
df['year'] = parts[0].astype('int')
df['month'] = parts[1].astype('int')
df['day'] = parts[2].astype('int')

from datetime import date
import holidays

def is_holiday(x):
  india_holidays = holidays.country_holidays('IN')
  if india_holidays.get(x):
    return 1
  else:
    return 0
  df['holidays'] = df['date'].apply(is_holiday)

  df.head()

# Check the columns in the DataFrame
print(df.columns)

# Drop only the columns that exist in the DataFrame
columns_to_drop = ['datetime', 'holiday', 'workingday', 'date']
existing_columns_to_drop = [col for col in columns_to_drop if col in df.columns]

# Drop the existing columns
df.drop(columns=existing_columns_to_drop, axis=1, inplace=True)

Index(['datetime', 'season', 'holiday', 'workingday', 'weather', 'temp',
       'atemp', 'humidity', 'windspeed', 'casual', 'registered', 'count',
       'date', 'time', 'year', 'month', 'day'],
      dtype='object')

df.head()

	datetime	season	holiday	workingday	weather	temp	atemp	humidity	windspeed	casual	registered	count	date	time	year	month	day
0	2011-01-01 00:00:00	1	0	0	1	9.84	14.395	81	0.0	3	13	16	2011-01-01	0	2011	1	1
1	2011-01-01 01:00:00	1	0	0	1	9.02	13.635	80	0.0	8	32	40	2011-01-01	1	2011	1	1
2	2011-01-01 02:00:00	1	0	0	1	9.02	13.635	80	0.0	5	27	32	2011-01-01	2	2011	1	1
3	2011-01-01 03:00:00	1	0	0	1	9.84	14.395	75	0.0	3	10	13	2011-01-01	3	2011	1	1
4	2011-01-01 04:00:00	1	0	0	1	9.84	14.395	75	0.0	0	1	1	2011-01-01	4	2011	1	1

df['time'].unique()

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23])

df.isnull().sum()

season        0
weather       0
temp          0
atemp         0
humidity      0
windspeed     0
casual        0
registered    0
count         0
time          0
year          0
month         0
day           0
dtype: int64

VISUAL DATA EXPLORATORY

numerical = df.drop(columns=["season","weather","time","day","month","year"],axis = 1, )
categorical = df[["season","weather","time","day","month","year"]]
numerical.head()

	temp	atemp	humidity	windspeed	casual	registered	count
0	9.84	14.395	81	0.0	3	13	16
1	9.02	13.635	80	0.0	8	32	40
2	9.02	13.635	80	0.0	5	27	32
3	9.84	14.395	75	0.0	3	10	13
4	9.84	14.395	75	0.0	0	1	1

sns.countplot(x='season', data=df)

<Axes: xlabel='season', ylabel='count'>

df['season'].value_counts()

season
4    2734
2    2733
3    2733
1    2686
Name: count, dtype: int64

We can see uniform distribution of bikes rented across four seasons.

sns.countplot(x='weather', data=df)

<Axes: xlabel='weather', ylabel='count'>

df['weather'].value_counts()

weather
1    7192
2    2834
3     859
4       1
Name: count, dtype: int64

We see that maximum bikes are rented when the weather is clear and partly cloudy.

sns.countplot(x='time', data=df)

<Axes: xlabel='time', ylabel='count'>

df['time'].value_counts()

time
16    456
17    456
18    456
19    456
12    456
13    456
14    456
15    456
20    456
21    456
22    456
23    456
8     455
6     455
7     455
0     455
10    455
9     455
11    455
1     454
5     452
2     448
4     442
3     433
Name: count, dtype: int64

Uniform distribution can be seen at all times of the day.

sns.countplot(x='day', data=df)

<Axes: xlabel='day', ylabel='count'>

df['day'].value_counts()

day
1     575
9     575
5     575
17    575
16    574
19    574
7     574
8     574
15    574
13    574
4     574
14    574
2     573
3     573
12    573
6     572
10    572
11    568
18    563
Name: count, dtype: int64

Uniform distribution can be seen at all the days.

sns.countplot(x='month', data=df)

<Axes: xlabel='month', ylabel='count'>

Uniform distribution can be seen across all the months.

sns.countplot(x='year', data=df)

<Axes: xlabel='year', ylabel='count'>

Equal number of bikes were rented in both the years.

sns.displot(x='temp', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be9d94c0>

We can see a normal distribution of bike rented across the temperature.

sns.displot(x='atemp', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be7a8ec0>

We can see a normal distribution of bike rented across the atemp.

sns.displot(x='humidity', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be7a9af0>

Here data is slightly skewed.

sns.displot(x='windspeed', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be962cc0>

df['windspeed'].value_counts()

windspeed
0.0000     1313
8.9981     1120
11.0014    1057
12.9980    1042
7.0015     1034
15.0013     961
6.0032      872
16.9979     824
19.0012     676
19.9995     492
22.0028     372
23.9994     274
26.0027     235
27.9993     187
30.0026     111
31.0009      89
32.9975      80
35.0008      58
39.0007      27
36.9974      22
43.0006      12
40.9973      11
43.9989       8
46.0022       3
47.9988       2
56.9969       2
51.9987       1
50.0021       1
Name: count, dtype: int64

Data is skewed. Count of bikes rented decreases as windspeed increases. Count is maximum when windspeed is zero.

sns.displot(x='casual', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be8ebb60>

df['casual'].value_counts()

casual
0      986
1      667
2      487
3      438
4      354
      ... 
294      1
280      1
216      1
292      1
304      1
Name: count, Length: 309, dtype: int64

Count of non registered user rentals(entry) of zero is maximum at 986 days followed by count of one, two and three user rentals most of the times. 309 is the maximum number of registrations that has been done one day.

sns.displot(x='registered', data=df)

<seaborn.axisgrid.FacetGrid at 0x218be7a3e60>

df['registered'].value_counts()

registered
3      195
4      190
5      177
6      155
2      150
      ... 
768      1
666      1
690      1
693      1
761      1
Name: count, Length: 731, dtype: int64

Count of registered user rentals(entry) of three is mazimum at 195 followed by four and five. 761 is the maximum number of registrations that has been done one day.

sns.displot(x='count', data=df, kde=True)

<seaborn.axisgrid.FacetGrid at 0x218beb8a4e0>

df['count'].value_counts()

count
5      169
4      149
3      144
6      135
2      132
      ... 
819      1
830      1
825      1
688      1
636      1
Name: count, Length: 822, dtype: int64

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='count')

<Axes: xlabel='time', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='casual')

<Axes: xlabel='time', ylabel='casual'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='registered')

<Axes: xlabel='time', ylabel='registered'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='count', hue='weather')

<Axes: xlabel='time', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='count', hue='season')

<Axes: xlabel='time', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='count', hue='workingday')

<Axes: xlabel='time', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='time', y='count', hue='holiday')

<Axes: xlabel='time', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.barplot(data=df, x='month', y='count')

<Axes: xlabel='month', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.barplot(data=df, x='season', y='count')

<Axes: xlabel='season', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.barplot(data=df, x='weather', y='count')

<Axes: xlabel='weather', ylabel='count'>

5 numer of bikes have been rented maximum number of days that is 169. The maximum number if bikes is 636 that has been rented one day.

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='registered', y='count')

<Axes: xlabel='registered', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='casual', y='count')

<Axes: xlabel='casual', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='temp', y='count')

<Axes: xlabel='temp', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='windspeed', y='count')

<Axes: xlabel='windspeed', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='humidity', y='count')

<Axes: xlabel='humidity', ylabel='count'>

fig, ax = plt.subplots(figsize=(20,10))
sns.pointplot(data=df, x='year', y='count')

<Axes: xlabel='year', ylabel='count'>

sns.boxplot(x='temp',data=df)

<Axes: xlabel='temp'>

sns.boxplot(x='atemp',data=df)

<Axes: xlabel='atemp'>

sns.boxplot(x='humidity',data=df)

<Axes: xlabel='humidity'>

There are few outliers in humidity data. This might be because of data entry errors or rare meteorological events can cause unusually high or low humidity levels.

sns.boxplot(x='windspeed',data=df)

<Axes: xlabel='windspeed'>

There are few outliers in windspeed data. This might be because of data entry errors or extreme weather phenomena that can cause extremely high windspeed readings.

sns.boxplot(x='casual',data=df)

<Axes: xlabel='casual'>

sns.boxplot(x='registered',data=df)

<Axes: xlabel='registered'>

sns.boxplot(x='count',data=df)

<Axes: xlabel='count'>

#treating outliers
outliers=df[df['windspeed']>32]
outliers=df[df['humidity']<10]
outliers.shape

(23, 13)

df=df[(df['windspeed']<32) & (df['humidity']>10)]
df.shape

(10636, 13)

corr = df.corr()

corr

	season	weather	temp	atemp	humidity	windspeed	casual	registered	count	time	year	month	day
season	1.000000	0.008688	0.251069	0.255650	0.170627	-0.117854	0.089204	0.160919	0.158798	-0.002001	-0.007863	0.971383	0.002861
weather	0.008688	1.000000	-0.057852	-0.058865	0.426167	-0.003800	-0.134406	-0.107356	-0.126598	-0.022993	-0.006757	0.010762	-0.008303
temp	0.251069	-0.057852	1.000000	0.985054	-0.077164	-0.003356	0.464794	0.315089	0.390958	0.148215	0.062043	0.250072	0.015292
atemp	0.255650	-0.058865	0.985054	1.000000	-0.056812	-0.041263	0.459791	0.311121	0.386268	0.144198	0.059383	0.255141	0.010752
humidity	0.170627	0.426167	-0.077164	-0.056812	1.000000	-0.303318	-0.363920	-0.280266	-0.334095	-0.279055	-0.089708	0.187304	-0.010524
windspeed	-0.117854	-0.003800	-0.003356	-0.041263	-0.303318	1.000000	0.104181	0.103729	0.115236	0.142263	-0.010875	-0.120907	0.035901
casual	0.089204	-0.134406	0.464794	0.459791	-0.363920	0.104181	1.000000	0.496717	0.690039	0.306292	0.144988	0.085978	0.015727
registered	0.160919	-0.107356	0.315089	0.311121	-0.280266	0.103729	0.496717	1.000000	0.970925	0.384322	0.261156	0.166388	0.021157
count	0.158798	-0.126598	0.390958	0.386268	-0.334095	0.115236	0.690039	0.970925	1.000000	0.404975	0.257774	0.162469	0.021981
time	-0.002001	-0.022993	0.148215	0.144198	-0.279055	0.142263	0.306292	0.384322	0.404975	1.000000	-0.002148	-0.002486	0.003051
year	-0.007863	-0.006757	0.062043	0.059383	-0.089708	-0.010875	0.144988	0.261156	0.257774	-0.002148	1.000000	-0.007670	0.003366
month	0.971383	0.010762	0.250072	0.255141	0.187304	-0.120907	0.085978	0.166388	0.162469	-0.002486	-0.007670	1.000000	0.003605
day	0.002861	-0.008303	0.015292	0.010752	-0.010524	0.035901	0.015727	0.021157	0.021981	0.003051	0.003366	0.003605	1.000000

corrmat =df.corr()
plt.figure(figsize=(10,10))
sns.heatmap(corrmat, annot=True,cmap='coolwarm',center=0)
plt.show()

sns.pairplot(df)

<seaborn.axisgrid.PairGrid at 0x218be88cc20>

#treatment of multicollinearity

df = df.drop(['temp','registered','month'],axis=1)

df.shape

(10636, 10)

MODELLING

PREPROCESSING FOR THE MODEL We want to predict the best model to count number of bikes rented and find features that are most important and affect count of bikes rented.

pip install scikit-learn

Requirement already satisfied: scikit-learn in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (1.5.1)
Requirement already satisfied: numpy>=1.19.5 in c:\users\ramasish chatterjee\appdata\local\programs\python\python312\lib\site-packages (from scikit-learn) (2.0.0)
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Note: you may need to restart the kernel to use updated packages.

Applying OLS and checking CLRM assumptions for linear regression

import pandas as pd

import statsmodels.api as sm
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from statsmodels.stats.outliers_influence import variance_inflation_factor
from statsmodels.stats.diagnostic import het_breuschpagan
from statsmodels.stats.stattools import durbin_watson

# Separate features and target variable
x = df.drop(columns=['count'], axis=1)
x = sm.add_constant(x)
y = df['count'].values

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.1, random_state=22)

# Fit the linear regression model

lr = sm.OLS(y_train, X_train).fit()
lr.params
lr.summary()

OLS Regression Results

Dep. Variable:	y	R-squared:	0.568
Model:	OLS	Adj. R-squared:	0.568
Method:	Least Squares	F-statistic:	1399.
Date:	Wed, 17 Jul 2024	Prob (F-statistic):	0.00
Time:	23:02:27	Log-Likelihood:	-59299.
No. Observations:	9572	AIC:	1.186e+05
Df Residuals:	9562	BIC:	1.187e+05
Df Model:	9
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	-1.267e+05	4953.191	-25.576	0.000	-1.36e+05	-1.17e+05
season	18.0748	1.158	15.611	0.000	15.805	20.344
weather	-5.8349	2.171	-2.688	0.007	-10.090	-1.580
atemp	1.5072	0.168	8.967	0.000	1.178	1.837
humidity	-0.6140	0.083	-7.377	0.000	-0.777	-0.451
windspeed	0.7209	0.174	4.137	0.000	0.379	1.062
casual	1.9242	0.030	63.177	0.000	1.864	1.984
time	5.4440	0.189	28.858	0.000	5.074	5.814
year	62.9861	2.462	25.580	0.000	58.160	67.813
day	0.3296	0.221	1.491	0.136	-0.104	0.763

Omnibus:	3805.039	Durbin-Watson:	1.997
Prob(Omnibus):	0.000	Jarque-Bera (JB):	15045.805
Skew:	1.984	Prob(JB):	0.00
Kurtosis:	7.688	Cond. No.	8.22e+06

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.22e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

#checking VIF for multicollinearity

vif_data = pd.DataFrame()
vif_data["feature"] = x.columns
vif_data["VIF"] = [variance_inflation_factor(x.values, i) for i in range(x.shape[1])]
print(vif_data)

     feature           VIF
0      const  1.667440e+07
1     season  1.120878e+00
2    weather  1.272024e+00
3      atemp  1.364249e+00
4   humidity  1.684794e+00
5  windspeed  1.138664e+00
6     casual  1.564723e+00
7       time  1.167136e+00
8       year  1.030064e+00
9        day  1.001633e+00

#Checking heteroscedasticity

from statsmodels.stats.diagnostic import het_goldfeldquandt
from sklearn.linear_model import LinearRegression

residuals = y_train - lr.predict(X_train)
#sorted residuals
sorted_residuals = np.sort(residuals)

#Find the split point for the subsets
split_index = int(len(sorted_residuals) * 0.5)

#Split the data into two subsets based on residuals
lower_half = sorted_residuals[:split_index]
upper_half = sorted_residuals[split_index:]

#Calculate the Goldfeld-Quandt test statistic and p-value 
gq_test_statistic, gq_p_value, _ = het_goldfeldquandt(y_train, X_train)

print("Goldfeld-Quandt test Statistic:", gq_test_statistic)
print("Goldfeld-Quandt Test p-value:", gq_p_value)

Goldfeld-Quandt test Statistic: 0.9086831174161009
Goldfeld-Quandt Test p-value: 0.9995303028283935

FEATURE SCALING

from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

from sklearn import metrics
from sklearn.metrics import accuracy_score, confusion_matrix, classification_report
from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error

ML MODELS

Linear Regression

from sklearn.linear_model import LinearRegression
lnr = LinearRegression()
lnr_model = lnr.fit(X_train_scaled, y_train)
lnr_pred = lnr.predict(X_test_scaled)
linear_r2 = r2_score(y_test, lnr_pred)
print("Linear Regression R2:", linear_r2)
linear_rmse = mean_squared_error(y_test, lnr_pred, squared=False)
print(linear_rmse)

Linear Regression R2: 0.5546065483357989
124.57231746528659

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

Decision Tree Regressor

from sklearn.tree import DecisionTreeRegressor
dt = DecisionTreeRegressor(random_state=42)
dt_model = dt.fit(X_train_scaled, y_train)
dt_pred = dt.predict(X_test_scaled)
tree_r2 = r2_score(y_test, dt_pred)
print("Decision Tree R2:", tree_r2)
tree_rmse = mean_squared_error(y_test, dt_pred, squared=False)
print(tree_rmse)

Decision Tree R2: 0.7442019049886539
94.4057143915263

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

Random Forest Regressor

from sklearn.ensemble import RandomForestRegressor
rfr = RandomForestRegressor(random_state=42)
rfr_model = rfr.fit(X_train_scaled, y_train)
rfr_pred = rfr.predict(X_test_scaled)
forest_r2 = r2_score(y_test, rfr_pred)
print("Random Forest R2:", forest_r2)
forest_rmse = mean_squared_error(y_test, rfr_pred, squared=False)
print(forest_rmse)

Random Forest R2: 0.8741353950924678
66.22186971657776

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

HYPERPARAMETER TUNING

from sklearn.model_selection import GridSearchCV

dt_params={'max_depth':[None,10,20,30],'min_samples_split':[2,5,10],'min_samples_split':[2,5,10]}
dt_grid=GridSearchCV(dt,dt_params,cv=5)
dt_grid.fit(X_train_scaled,y_train)

GridSearchCV(cv=5, estimator=DecisionTreeRegressor(random_state=42),
             param_grid={'max_depth': [None, 10, 20, 30],
                         'min_samples_split': [2, 5, 10]})

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dt_result=pd.DataFrame(dt_grid.cv_results_)
best_parameters_dt=dt_grid.best_params_
print(best_parameters_dt,dt_grid.best_score_)

{'max_depth': 10, 'min_samples_split': 10} 0.8129806416327222

ran_forest_params={'n_estimators':[50,100,200],'max_depth':[None,10,20,30],'min_samples_split':[2,5,10],'min_samples_split':[2,5,10]}
ran_forest_grid=GridSearchCV(rfr,ran_forest_params,cv=5)
ran_forest_grid.fit(X_train_scaled,y_train)

GridSearchCV(cv=5, estimator=RandomForestRegressor(random_state=42),
             param_grid={'max_depth': [None, 10, 20, 30],
                         'min_samples_split': [2, 5, 10],
                         'n_estimators': [50, 100, 200]})

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ran_forest_result=pd.DataFrame(ran_forest_grid.cv_results_)
best_parameters_ran_forest=ran_forest_grid.best_params_
print(best_parameters_ran_forest,ran_forest_grid.best_score_)

{'max_depth': 20, 'min_samples_split': 2, 'n_estimators': 200} 0.8658644179383306

Final Models

from sklearn.metrics import roc_curve

lnr = LinearRegression(fit_intercept=True, copy_X=True, n_jobs=None)
lnr_model = lnr.fit(X_train_scaled, y_train)
lnr_pred = lnr.predict(X_test_scaled)
linear_r2 = r2_score(y_test, lnr_pred)
print("Linear Regression R2:", linear_r2)
linear_rmse = mean_squared_error(y_test, lnr_pred, squared=False)
print(linear_rmse)

Linear Regression R2: 0.5546065483357989
124.57231746528659

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

dtf=DecisionTreeRegressor(max_depth= 10, min_samples_split= 10)
dtf.fit(X_train_scaled,y_train)
y_pred_dtf=dtf.predict(X_test_scaled) 
tree_r2 = r2_score(y_test, y_pred_dtf)
print("Decision Tree R2:", tree_r2)
tree_rmse = mean_squared_error(y_test, y_pred_dtf, squared=False)
print(tree_rmse)

Decision Tree R2: 0.8189796347652459
79.41697641736782

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

ran_forestf=RandomForestRegressor(n_estimators = 200, max_depth = 20, min_samples_split = 2)
ran_forestf.fit(X_train_scaled,y_train)
y_pred_ran_forest_f=rfr.predict(X_test_scaled) 
forest_r2 = r2_score(y_test, y_pred_ran_forest_f)
print("Random Forest R2:", forest_r2)
forest_rmse = mean_squared_error(y_test, y_pred_ran_forest_f, squared=False)
print(forest_rmse)

Random Forest R2: 0.8741353950924678
66.22186971657776

C:\Users\Ramasish Chatterjee\AppData\Local\Programs\Python\Python312\Lib\site-packages\sklearn\metrics\_regression.py:492: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

Feature Importance

# Get the feature importances
importances = ran_forestf.feature_importances_

# Convert X_train_scaled back to DataFrame to get column names
X_train_scaled_df = pd.DataFrame(X_train_scaled, columns=X_train.columns)

# Map the feature importances to their corresponding feature names
feature_importance_df = pd.DataFrame({
    'Feature': X_train_scaled_df.columns,
    'Importance': importances
}).sort_values(by='Importance', ascending=False)

# Display the feature importances
print(feature_importance_df)

# Plot the feature importances
plt.figure(figsize=(10, 8))
sns.barplot(x='Importance', y='Feature', data=feature_importance_df)
plt.title('Feature Importances from Random Forest Regressor')
plt.xlabel('Importance')
plt.ylabel('Feature')
plt.show()

     Feature  Importance
6     casual    0.595181
7       time    0.231478
8       year    0.045469
3      atemp    0.036505
4   humidity    0.030343
1     season    0.018919
9        day    0.018767
5  windspeed    0.016948
2    weather    0.006391
0      const    0.000000